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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 490392n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490392.n1 | 490392n1 | \([0, 0, 0, -550515, 157215422]\) | \(210094874500/3753\) | \(329605378163712\) | \([2]\) | \(3096576\) | \(1.9128\) | \(\Gamma_0(N)\)-optimal |
490392.n2 | 490392n2 | \([0, 0, 0, -532875, 167760614]\) | \(-95269531250/14085009\) | \(-2474017968496822272\) | \([2]\) | \(6193152\) | \(2.2593\) |
Rank
sage: E.rank()
The elliptic curves in class 490392n have rank \(1\).
Complex multiplication
The elliptic curves in class 490392n do not have complex multiplication.Modular form 490392.2.a.n
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.